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@restrepo restrepo/upmns.py
Last active May 9, 2018

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import numpy as np
def neutrino_data():
'''From arxiv:1405.7540 (table I)
and asumming a Normal Hierarchy:
Output:
mnu1in: laightest neutrino mass
Dms2: \Delta m^2_{12}
Dma2: \Delta m^2_{13}
ThetSol,ThetAtm,ThetRec: in radians
'''
Dms2=np.array([7.11e-5, 7.60e-5, 8.18e-5])*1e-18 # In GeV
Dma2=np.array([2.30e-3, 2.48e-3, 2.65e-3])*1e-18 # In GeV
#input real values:
#
ThetSol = np.array([0.278, 0.323, 0.375])
ThetAtm = np.array([0.392, 0.567, 0.643])
ThetRec = np.array([0.0177, 0.0234, 0.0294])
mnu1in=1E-5*1E-9
return mnu1in,Dms2,Dma2,ThetSol,ThetAtm,ThetRec
def CasasIbarra(ranMnu=True,bestfit=True):
#import numpy as np
if ranMnu==True:
bestfit=True
mnu1in,Dms2,Dma2,ThetSol,ThetAtm,ThetRec=neutrino_data()
# Phases of the PMNS matrix
phases1=np.random.uniform(0.,0.0*np.pi,3) # cero value for all phases
delta=1.*(0 if ranMnu else phases1[0])
eta1 =1.*(0 if ranMnu else phases1[1])
eta2 =1.*(0 if ranMnu else phases1[2])
mnu1=1.*(mnu1in if bestfit else 10**((np.log10(2.5e-3)-np.log10(1e-9))*np.random.uniform(0,1)+np.log10(1e-9))*1e-9)
mnu2=1.*(np.sqrt(Dms2[1]+mnu1in**2) if bestfit else np.sqrt(np.random.uniform(Dms2[0],Dms2[2]) + mnu1**2) )
mnu3=1.*(np.sqrt(Dma2[1]+mnu1in**2) if bestfit else np.sqrt(np.random.uniform(Dma2[0],Dma2[2]) + mnu1**2) )
# Square root of left-handed neutrino mass matrix
DMnu = np.diag( [np.sqrt(mnu1),np.sqrt(mnu2),np.sqrt(mnu3)] )
#print "NEUTRINOS",mnu1,mnu2,mnu3
# Mixing angles (up 3 sigma range)
t12 = 1.*( np.arcsin(np.sqrt(ThetSol[1])) if bestfit else np.arcsin(np.sqrt(np.random.uniform(ThetSol[0],ThetSol[2]))))
t23 = 1.*( np.arcsin(np.sqrt(ThetAtm[1])) if bestfit else np.arcsin(np.sqrt(np.random.uniform(ThetAtm[0],ThetAtm[2]))))
t13 = 1.*( np.arcsin(np.sqrt(ThetRec[1])) if bestfit else np.arcsin(np.sqrt(np.random.uniform(ThetRec[0],ThetRec[2]))))
# Building PMNS matrix
U12 = np.array([ [np.cos(t12), np.sin(t12),0], [-np.sin(t12), np.cos(t12),0], [0,0,1.0] ])
U13 = np.array([ [np.cos(t13),0, np.sin(t13)* np.exp(-delta*1j)], [0,1.0,0], [-np.sin(t13)*np.exp(delta*1j),0, np.cos(t13)] ])
U23 = np.array([ [1.0,0,0], [0, np.cos(t23), np.sin(t23)], [0, -np.sin(t23), np.cos(t23)] ])
Uphases = np.array([ [np.exp(eta1*1j),0,0], [0, np.exp(eta2*1j),0], [0,0,1.0] ])
U = np.dot(U23,np.dot(U13,np.dot(U12,Uphases)))
return U
if __name__=='__main__':
print( CasasIbarra(ranMnu=True) )
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